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At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?

Correct answer: C. 44

  • A. 38
  • B. 40
  • C. 44
  • D. 48

Explanation

The trains travel for 3.5 hours, so their combined speed is 287 miles / 3.5 hours = 82 miles per hour. If the slower speed is s miles per hour, the faster speed is s + 6 miles per hour; hence 2s + 6 = 82, giving s = 38 miles per hour and faster speed = 44 miles per hour. The likely wrong choice is 38 miles per hour, which is the slower train's speed, not the faster train's speed.

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About Time, Speed and Distance

Problems relate distance, speed and time through the formula distance = speed × time, including unit conversion, average speed, relative speed and motion in opposite or the same direction. Questions may involve trains, boats and streams, where the effective speed changes, so average speed must not be confused with the simple average of two speeds.

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